Unified strength theory


The unified strength theory. proposed by Yu Mao-Hong is a series of yield criteria and failure criteria. It is a generalized classical strength theory which can be used to describe the yielding or failure of material begins when the combination of principal stresses reaches a critical value.

Mathematical Formulation

Mathematically, the formulation of UST is expressed in principal stress state as
where are three principal stresses, is the uniaxial tensile strength and is tension-compression strength ratio.
The unified yield criterion is the simplification of UST when, i.e.



Limit surfaces of Unified Strength Theory

The limit surfaces of the unified strength theory in principal stress space are usually a semi-infinite dodecahedron cone with unequal sides. The shape and size of the limiting dodecahedron cone depends on the parameter b and. The limit surfaces of UST and UYC are shown as follows.

Derivation of Unified Strength Theory

Due to the relation, the principal stress state may be converted to the twin-shear stress state or. Twin-shear element models proposed by Mao-Hong Yu are used for representing the twin-shear stress state. Considering all the stress components of the twin-shear models and their different effects yields the unified strength theory as
The relations among the stresses components and principal stresses read
The and C should be obtained by uniaxial failure state
By substituting Eqs., and into the Eq., and substituting Eqs., and into Eq., the and C are introduced as

History of Unified Strength Theory

The development of the unified strength theory can be divided into three stages as follows.
1. Twin-shear yield criterion
2. Twin-shear strength theory.
3. Unified strength theory.

Applications of the Unified Strength theory

Unified strength theory has been used in Generalized Plasticity, Structural Plasticity, Computational Plasticity and many other fields